主子阵约束下的Hermite广义反Hamilton矩阵的广义特征值反问题  

Inverse Generalized Eigenvalue Problem for Hermite Generalized Inverse Hamilton Matrix under a Submatrix Constraint

作　　者：李玉洁 Li Yujie(Institute of Mathematics and Statistics,Anhui Normal University,Wuhu 241003,China)

机构地区：[1]安徽师范大学数学与统计学院,安徽芜湖241003

出　　处：《湖南科技大学学报（自然科学版）》2020年第1期113-118,共6页Journal of Hunan University of Science And Technology：Natural Science Edition

摘　　要：利用矩阵分块和矩阵商奇异值分解,给出了主子阵约束下的Hermite广义反Hamilton矩阵的广义特征值反问题有解的充要条件和通解具体表达式.并讨论了用主子阵约束下的广义特征值反问题的Hermite广义反Hamilton解来构造给定矩阵的最佳逼近解问题,得出该问题有解的充分必要条件和最佳逼近解的表达式.Using matrix factorization and quotient singular value decomposition of a matrix,the necessary and sufficient conditions,that of the existence of solution,were given to inverse genera-lized eigenvalue problem for hermite generalized inverse hamilton matrices under a submatrix constraint,the expression for the solution was provided.Moreover,based on solution set of inverse generalized eigenvalue problem for hermite generalized inverse hamilton matrices under a submatrix constraint,the optimal approxition problem to a given matrix was considered,the necessary and sufficient conditions for the optimal approxition problem are given,and the expression for the solution was provided.

关 键 词：Hermite广义反Hamilton矩阵 广义特征值反问题 最佳逼近 

分 类 号：O151.21[理学—数学]